This book is a reference and user's guide for Combinatorica, an extension to Mathematica that is used for teaching and research in discrete mathematics. Included are examples of all 450 Combinatorica functions as well as associated mathematical and algorithmic theory. These functions are available for active experimentation and visualization with the aim of advancing the study of combinatorics and graph theory. The text covers classical and advanced topics on the most important combinatorial objects and all important areas of graph theory and can be used for self-study or in discrete mathematics courses.